Glossy paper on cycles
To get these directional reflections its best to use a Anisotropic Shader, it yields those as a result and you can change certain properties of it:





This is the node tree that i've used:



Depending on the look and feel you want to produce you can play around with the settings of the anisotropic shader. To turn the effect down, simple change the factor of the mix node.

To get the small surface effects printed paper sometimes has, i've implemented a simple voroni noice as a normal in the anisotropic node. It adds a small level of detail that could be needed on close shots. It's not perfect and more meant as an example as to what is possible.

Note: It's also possible to use the built in anisotropic settings in the principled bsdf - i just like to use it seperated.